Massimiliano Allegri's side have already seen a €15 million bid knocked back, with Danilo and Federico Bernardeschi also summer transfer targetsJuventus want to sign Blaise Matuidi but will have to up their initial offer of €15 million to land the PSG star,
The France international midfielder is in the final year of his contract that expires in 2018 although the Ligue 1 club are unwilling to sell the 30-year-old for less than €30m.
PSG are reluctant to allow Matuidi to leave and have offered him a new contract to remain at Parc des Princes, with the player himself still undecided.
Unai Emery's side lost their grip on the Ligue 1 title in 2016-17 as Monaco claimed their first league win in 17 years.
Juventus, meanwhile, won Serie A for the sixth successive season and reached the final of the Champions League, where they were beaten by Real Madrid.
Publicly Matuidi, who has also been heavily linked with a move to Manchester United, has kept his cards close to his chest in regards to his future.
When asked about a possible exit from PSG back in June, he told reporters that his sole focus was the international friendly meeting with England and added: "As for PSG [and talk of leaving], I have nothing else to say about it."
Aside from Matuidi, Massimiliano Allegri has also included Real Madrid full-back Danilo and Federico Bernardeschi as part of his list of summer transfer targets.
As revealed by Goal in June, Juve made an initial offer of €15m plus bonuses for Danilo, but Madrid are hoping to secure a fee of €30m for the right-back.